Torsional quartz crystal resonator

ABSTRACT

A torsional quartz crystal resonator has a specific cut type resulting in improved frequency temperature behavior. The cut type is defined by rotating a Z plate quartz crystal around an x-axis at an angle  phi  in the range of 0 DEG  through 30 DEG  and by further rotating the plate around a z&#39;-axis at another angle  theta  in the range of -20 DEG  through -10 DEG  or +10 DEG  through +20 DEG . The resonator has a thickness z0 and a width x0 determined such that a thickness-to-width ratio Rzx=z0/x0 is set within the range of 0.6 through 1.1 to make the first order temperature coefficient substantially zero in combination with the optimum angles  phi  and  theta . Excitation electrodes are disposed on major faces of the resonator normal to the z&#39; axis, and a connecting electrode is disposed on a side face of the resonator to reduce the series resistance R1.

This is a continuation of application Ser. No. 886,330 filed May 20,1992, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a torsional quartz crystal resonator.More specifically, the invention relates to the cut angle,thickness-to-width ratio, shape and excitation electrode structure of atorsional quartz crystal resonator of the specific cut type referred toas "TT cut" in this description. The present invention particularlyrelates to the torsional quartz crystal resonator of the type suitablefor a clock signal source in various portable devices such as a wristwatch, a pager, an IC card and a vehicle wireless communicationimplement, in which the resonator is required to have a high level ofaccuracy, a compact size, good resistance to shock and a reasonableprice.

2. Description of the Prior Art

There has been used in the prior art a flexural mode quartz crystalresonator of a tuning fork type, and a length extensional mode quartzcrystal resonator in a frequency band of 200 kHz-600 kHz. However, theflexural mode quartz crystal resonator of the tuning fork type utilizesan overtone, and hence formation of electrodes is complicated and aserious loss of vibrational energy is caused through lead wires, etc.Consequently, this type of resonator has the drawback of a relativelyhigh series resistance R₁. On the other hand, the extensional modequartz crystal resonator has an oscillating frequency which isreciprocal to a length of a vibrational arm of the resonator. Therefore,the resonator is enlarged in the relatively low frequency range below600 kHz, thereby causing the drawback that the ability scale-down theresonator in size is difficult. In view of these drawbacks, there haslong been desired a quartz crystal resonator of a new cut type whichwould feature an oscillating frequency in the range of 200 kHz-600 kHz,a micronized compact size, a zero temperature coefficient, and an easychemical etching process.

SUMMARY OF THE INVENTION

An object of the invention is to provide a torsional quartz crystalresonator of a new cut type, defined by rotating a Z plate quartzcrystal around the x-axis and further rotating the quartz crystal aroundthe z'-axis.

Another object of the invention is to set an optimum range of thethickness-to-width ratio in a torsional quartz crystal resonatorresulting in good frequency temperature behavior. Namely, the frequencytemperature behavior can be improved by optimally setting the ratio ofthe thickness to the width of the resonator.

A further object of the invention is to provide an excitation electrodestructure having a reduced series resistance. Namely, the seriesresistance can be reduced by arranging the excitation electrode on aface of the resonator piece, normal to the z'-axis, and by arranging aconnection electrode on a side face of a vibrational portion of theresonator.

A still further object of the invention is to provide a torsional quartzcrystal resonator having a specific configuration effective to reduce aloss of vibration energy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing the coordinate system of theinventive torsional quartz crystal resonator;

FIG. 2A is a graph showing the relation between cut angles φ, θ and athickness-to-width ratio Rzx of the inventive torsional quartz crystalresonator in which the first order temperature coefficient α is set tozero;

FIG. 2B is a graph showing the relation between the second ordertemperature coefficient β and the cut angle φ in the FIG. 2A resonator;

FIG. 3A is another graph showing the relation between the cut angles φ,θ and the thickness-to-width ratio Rzx while the first order temperaturecoefficient α is set to zero;

FIG. 3B is another graph showing the relation between the second ordertemperature coefficient β and the cut angle φ in the FIG. 3A resonator;

FIG. 4 is a graph showing an example of the frequency temperaturebehavior of the inventive torsional quartz crystal resonator of thetuning fork type;

FIG. 5 is a graph showing another example of the frequency temperaturebehavior of the inventive torsional quartz crystal resonator of thetuning fork type;

FIG. 6A is a schematic diagram showing the torsional quartz crystalresonator of the tuning fork type formed from a quartz crystal platehaving cut angles φ, θ determined according to the invention;

FIG. 6B is a sectional diagram showing the electrode structure of theFIG. 6A resonator;

FIG. 7 is an overall view showing a shape and an excitation electrodearrangement of another embodiment of the inventive torsional quartzcrystal resonator;

FIG. 8 is a graph showing the relation between a piezoelectric constante₁₆ and the cut angle φ of the inventive resonator, where the other cutangle θ is set as a parameter; and

FIG. 9 is a graph showing the relation between the cut angle φ and thefrequency constant f.y₀, where the other cut angle θ is set as aparameter in the inventive torsional quartz crystal resonator of thetuning fork type.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows the coordinate system of the inventive torsional quartzcrystal resonator. The coordinate system 0-xyz is comprised of an originpoint 0, an electrical axis x, a mechanical axis y and an optical axisz. An original torsional quartz crystal resonator 1 has a thickness z₀,a width x₀ and a length y₀ and a torsional moment around the y axis.This original resonator is defined along a Z plate quartz crystal whichis normal to the z axis. Then, referring to FIG. 6A, the originalresonator is rotated around the x axis by an angle φ in the range from-90° to +90°, where a counterclockwise direction is denoted by a plussign, such that the rotated resonator has a new z axis, i.e., z' axis.Further, the resonator is rotated around the z' axis by another angle θin the range of -80° through -10° or in the range of 10° through 80°,hereinafter referred to in abbreviated form as ±(10° through 80°),thereby defining the inventive resonator of a new cut which ishereinafter referred to as "TT cut".

The cut angles φ, θ and the thickness-to-width ratio Rzx=z₀ /x₀ areoptimally determined to set the first order temperature coefficient α tozero. FIG. 2A shows the relation between the cut angles φ, θ and thethickness-to-width ratio Rzx, which are set to establish the conditionthat the first order temperature coefficient α equals zero in theinventive torsional quartz crystal resonator. FIG. 2B shows the relationbetween the second order temperature coefficient β and the cut angle φunder the condition α=0. These graphs indicate calculated values whilethe cut angle θ is set to 0°, ±10°, ±20° and ±30° as a parameter, andmeasured values where the cut angle θ is fixed to ±10° and ±30°. Asunderstood from the FIG. 2A graph, the condition α=0 can be establishedby suitably selecting the thickness-to-width ratio Rzx while the cutangle φ ranges from -50° through +60° when θ=±(0° through 30°). Further,as seen in FIG. 2B, the absolute value of β takes a minimum level aroundφ=30° when the cut angle θ is set to ±10°. For example, while α=0 isheld when φ=28° and θ=±10°, the calculated value of β is -1.16×10⁻⁸/°C.² and the measured value of β is - 1.29×10⁻⁸ /°C.² with respect tothe resonator of the tuning fork type. The absolute value of thecalculated and measured β is significantly smaller than that of theflexural mode quartz crystal resonator (β=-3.8×10⁻⁸ /°C.²) by aboutone-third. Further, the condition α=0 is held at φ=-42° and θ=±30°,while the calculated value of β is -1.06×10⁸ /°C.² and the measuredvalue of β is -1.22×10⁻⁸ /°C.². In this case, the absolate value of βcan be significantly reduced. In general, the condition α=0 is obtainedin the range of φ=-50° through +60° by suitably setting the other cutangle θ and the thickness-to-width ratio Rzx, while the value of β isreduced in the range of -1.2×10⁻⁸ /°C.² through -3.7×10⁻⁸ /°C.². Sincethe absolute value of β can be made small, there can be obtained atorsional quartz crystal resonator exhibiting excellent frequencytemperature behavior.

FIGS. 3A and 3B show the similar relations as the FIGS. 2A and 2B graphsfor the same torsional quartz crystal resonator of the tuning fork type,where the parametric cut angle θ is further set greater to ±40°, ±60°and ±80°. Namely, the FIG. 3A graph shows the relation between the cutangles φ, θ and the thickness-to-width ratio Rzx, set to satisfy thecondition α=0. FIG. 3B shows the value of the second order temperaturecoefficient β under the condition α=0. Except for the range of aroundα=35° where the condition α=0 is not realized, the condition α=0 can beachieved generally in the range of φ=90° through +90° by suitablyselecting the thickness-to-width ratio Rzx. Further, as seen from FIG.3B, the value β can take a relatively low value in the range of-1.0×10⁻⁸ /°C.² through -3.8×10⁻⁸ /°C.² as in the case of θ=±(0° through30°), thereby obtaining a torsional quartz crystal resonator of thetuning fork type exhibiting good frequency temperature behavior.

According to the invention, the condition α=0 can be established byselecting the cut angle φ in the range of -90° through +90°, byselecting the other cut angle θ in the range of ±(10° through 80°) andby selecting the ratio Rzx in the range of 0.1 through 1.5. Typicaltemperature behavior of the thus defined resonator is shown in FIGS. 4and 5. FIG. 4 is a graph showing one example of the frequencytemperature behavior of the tuning fork type inventive torsional quartzcrystal resonator having cut angles of φ=28° and θ=10°. The solid linecurve indicates the calculated value of the frequency deviation Δf/f,and circle points indicate the measured values. On the other hand, thebroken line curve indicates the frequency temperature behavior of theconventional flexural mode quartz crystal resonator. As appreciated fromthe FIG. 4 graph, the inventive torsional quartz crystal resonator ofthe tuning fork type exhibits better frequency temperature behavior.

FIG. 5 shows another example of the frequency temperature behavior ofthe inventive tuning fork type quartz crystal resonator having the cutangles of φ=-42° and θ=30°. As in the FIG. 4 case, it is understood fromthe FIG. 5 graph that the inventive tuning fork type torsional quartzcrystal resonator has better frequency temperature behavior as comparedto the conventional flexural mode quartz crystal resonator.

FIG. 6A shows a perspective view of the tuning fork type torsionalquartz crystal resonator formed from a quartz crystal plate having thecut angles φ, θ set according to the invention. FIG. 6B shows a sectionof the same resonator, illustrating the electrode structure. Theresonator has a pair of electrode terminals A and B. The one terminal Ais connected to electrodes 2, 5, 7 and 8, and the other terminal B isconnected to electrodes 3, 4, 6 and 9. In this electrode structure, theinventive torsional quartz crystal resonator 10 is excited according toa piezoelectric constant e₁₆. FIG. 8 shows the relation betweenpiezoelectric constant e₁₆ and the cut angles φ, θ.

FIG. 7 is a perspective view showing a shape and an exciting electrodearrangement of another embodiment of the inventive torsional quartzcrystal resonator. A resonator 11 is comprised of a vibrational portion12 having exciting electrodes 17, 18, 21 and 22 (the electrodes 21 and22 being hidden from the view) and connecting electrodes 19, 20 (theelectrode 20 is hidden from the view), and a supporting portion 13connected to the vibrational portion through a pair of bridge portions14. The supporting portion 13 is comprised of a frame 15 coupled to thebridge portions 14 disposed at the central part of the vibrationalportion 12, and coupled to a mount 16. Further, the exciting electrode17 is formed on a top face of the vibrational portion 12. The connectingelectrode 20 is disposed on an etched face which is formed by an etchingprocess for connecting the exciting electrode 17 and the other excitingelectrode 21 (not shown) which is formed on a bottom face of thevibrational portion 12 in opposed relation to the front excitingelectrode 18. In similar manner, the front exciting electrode 18 isconnected to the rear exciting electrode 22 (not shown) formed inopposed relation to the front exciting electrode 17, through the otherconnecting electrode 19 formed on the etched face. The pair of excitingelectrodes 17, 18 of opposite polarities are extended along the frame 15to the mount 16 for external electrical connection. An alternatingvoltage is applied between the end terminals of the pair of excitingelectrodes 17, 18 to efficiently induce a torsional vibration. By suchconstruction of the resonator, the series resistance R₁ can be lowered,while the vibrational energy can be confined efficiently within thevibrational portion 12, thereby providing an improved quartz crystalresonator having excellent electric characteristics, free of vibrationalleak. Further, though the inventive resonator has a rather complicatedshape, the resonator can be formed easily by chemical etching.

FIG. 8 shows the relation between the piezoelectric constant e₁₆ and thecut angle φ while the other cut angle θ is set as a parameter. As seenfrom the graph, the piezoelectric constant e₁₆ becomes zero at θ=0° inthe entire range of the cut angle φ, hence and the present torsionalquartz crystal resonator can not be excited. However, the absolute valueof e₁₆ gradually increases as the cut angle θ increases, so that theconstant e₁₆ has a maximum value at θ=30°. Though not shown in thefigure, when the cut angle θ is further increased, the absolute value ofe₁₆ reversely and gradually decreases so that the absolute value of e₁₆becomes minimum at θ=60°. When the cut angle θ is still furtherincreased, the absolute value of e₁₆ again increases. As understood fromthe above description, the torsional quartz crystal resonator having thecut angle θ=0° is not excited by the inventive electrode structure.Further, the absolute value of e₁₆ is extremely small in the cut anglerange below θ=10°, hence the series resistance R₁ is rather great and istherefore not practical. Accordingly, the absolute cut angle θ is setnot less than 10° so as to lower the series resistance R₁ in theinvention.

Next, the description is given for micronization of the resonator. FIG.9 shows the relation between the cut angle φ and the frequency constantf.y₀ with respect to the inventive tuning fork type torsional quartzcrystal resonator having the thickness-to-width ratio Rzx=0.8, where theother cut angle θ is set as a parameter. Although depending on thevalues of the cut angles φ, θ, the frequency constant ranges from 80 to97 kHz.cm, which is greater than the typical value of 7.9 kHz.cm of theconventional tuning fork type flexural quartz crystal resonator havingthe thickness-to-width ratio of 0.1, and which is smaller than thetypical value of 270 kHz.cm of the conventional length extensional modequartz crystal resonator. Namely, the frequency constant of theinventive tuning fork type torsional quartz crystal resonator rangesbetween those of the flexural mode and the length extensional mode, sothat the inventive resonator is particularly suitable for use in thefrequency range from 200 kHz to 600 kHz.

Next, the description is given for the typical electrical equivalentcircuit parameters of the inventive tuning fork type torsional quartzcrystal resonator. Table 1 shows the typical parameters with respect todifferent samples of the inventive tuning fork type torsional quartzcrystal resonator, having the cut angles φ=0°, θ=30° and the other cutangles φ=26°, θ=10°. In case of φ=0° and θ=30°, the following data areobtained: frequency f=444.1 kHz, R₁ =2.2 kΩ and Q=378,000. On the otherhand, in case of φ=26°, θ=10°, the following data are obtained: f=385.8kHz, R₁ =14.4 kΩ and Q=276,000. Accordingly, there can be obtained aresonator having a small value of R₁ and great value of Q. Further, itis understood from the value of e₁₆ that the excellent R₁ and Q valuescan be obtained in the various cut angle ranges of φ and θ besides thelisted samples.

                                      TABLE 1                                     __________________________________________________________________________    φ                                                                              θ                                                                             f     R.sub.1                                                                            L.sub.1                                                                           Q    C.sub.0                                        (DEG.)                                                                             (DEG.)                                                                              (kHz) (kΩ)                                                                         (kH)                                                                              (× 10.sup.3)                                                                 (pF)                                                                             r                                           __________________________________________________________________________     0   30    444.1  2.2 0.30                                                                              378  0.425                                                                             984                                        26   10    385.8 14.4 1.64                                                                              276  0.434                                                                            4190                                        __________________________________________________________________________

As described above, the inventive torsional quartz crystal resonator ofthe TT cut can produce the following remarkable effects:

(1) The cut angle φ is set in the range from -90° to +90°, the other cutangle θ is set in the range of ±(10° through 80°) and thethickness-to-width ratio Rzx is set in the range of 0.1 through 1.5,such that the first temperature coefficient α is made zero to therebyachieve excellent frequency temperature behavior.

(2) Particularly, the cut angles φ, θ and the thickness-to-width ratioRzx are optimumly set to reduce the second order temperature coefficientβ by about one-third of the conventional tuning type flexural modequartz crystal resonator, thereby reducing variation of the frequencyrelative to the temperature as compared to the flexural mode and thelength extensional mode.

(3) The inventive resonator can be formed easily by an etching processwhen the cut angle φ ranges from -55° to +30° and the other cut angle θranges ±(10° through 80°), thereby reducing the size and the thicknessof the resonator. Additionally, a plurality of resonator pieces can beproduced at once by the batch processing of one wafer, thereby loweringthe production cost.

(4) The inventive resonator has a frequency range between thefundamental vibration mode of the tuning type flexural quartz crystalresonator and the length extensional mode quartz crystal resonator,thereby making the inventive resonator particularly suitable to therange of 200 kHz through 600 kHz.

(5) The invention can facilitate the micronization of the quartz crystalresonator.

(6) The exciting electrodes are disposed on the top and bottom faces ofthe resonator piece, thereby decreasing the series resistance R₁ andincreasing the Q value of the torsional quartz crystal resonator.

(7) The inventive resonator can be shaped as the tuning fork type or thefree-free bar type such that the vibrational portion can be formedintegrally with the supporting portion, thereby reducing a loss ofvibrational energy which would be otherwise caused by lead wires, toproduce a torsional quartz crystal resonator having good shockresistance.

What is claimed is:
 1. A torsional quartz crystal tuning fork resonatorvibratable in a torsional mode, the resonator having a specific cut typedefined such that a Z plate quartz crystal normal to a z-axis (opticalaxis) and having its length extending along a y-axis (mechanical axis)is rotated around an x-axis (electrical axis) by a cut angle φ in therange of 0° through +30°, and is further rotated around a resultantz'-axis (new z-axis) by another cut angle θ in the range of -20° through-10° or +10° through +20° so as to form the torsional quartz crystaltuning fork resonator, the resonator having a thickness-to-width ratioR_(zx) =z₀ /x₀ within the range of 0.6 through 1.1, and the resonatorhaving a first order temperature coefficient α of approximately zeroaround room temperature.
 2. A torsional quartz crystal tuning forkresonator according to claim 1; including an excitation electrodedisposed on a given face of the resonator, which is normal to the z'axis.
 3. A torsional quartz crystal tuning fork resonator vibratable ina torsional mode, comprising: a vibrational portion having a tuning forkshape having top and bottom faces; a bridge portion connected to anintermediate part of the vibrational portion; a supporting portionconnected to the bridge portion and having a mount on an end of thesupporting portion; and a pair of excitation electrodes of oppositepolarities disposed on at least one of the top and bottom faces of thevibrational portion adjacent to one another; wherein the resonator isformed from a quartz crystal plate which is defined by rotating a Zplate around an x-axis at an angle in the range of 0° through +30° andby further rotating the same around a z'-axis at another angle in therange of -20° through -10° or +10° through 20°, the resonator having athickness-to-width ratio R_(zx) =z₀ /x₀ within the range of 0.6 through1.1, and the resonator having a first order temperature coefficient α ofapproximately zero around room temperature.
 4. A torsional quartzcrystal tuning fork resonator according to claim 3; wherein thevibrational portion and the support portion are formed integrally withone another by chemical etching of the Z plate.
 5. A torsional quartzcrystal tuning fork resonator according to claim 3; including aconnecting electrode arranged on an etched side face of the vibrationalportion for forming a connection between excitation electrodes disposedon top and bottom faces of the vibrational portion.
 6. A torsionalquartz crystal tuning fork resonator, comprising: a tuning fork having aplurality of tines vibratable in a torsional mode of vibration duringuse of the resonator, the tuning fork comprising a quartz crystal Z-cutplate having x, y and z axes corresponding, respectively, to theelectrical, mechanical and optical axes of the quartz crystal, the platehaving a length defined along the y-axis, a width x₀ defined along thex-axis and a thickness z₀ defined along the z-axis, the fork tinesextending lengthwise along the y-axis, and the cut of the plate beingdefined by rotation of the plate through a first cut angle in the rangeof 0° through +30° around the x-axis thereby defining new x', y' and z'axes, and rotation of the plate through a second cut angle in the rangeof -20° through -10° or +10° through +20° around the z' axis to form aquartz crystal tuning fork resonator having a thickness-to-width ratioR_(zx) =z₀ /x.sub. 0 within the range of 0.6 through 1.1 and having afirst order temperature coefficient α of approximately zero around roomtemperature.
 7. A torsional quartz crystal tuning fork resonator,comprising: a quartz crystal Z-cut plate having x, y and z axescorresponding to the electrical, mechanical and optical axes,respectively, of the quartz crystal, the cut of the plate being definedby rotation of the plate around the x-axis through an angle in the range0° through +30° thereby defining new x', y' and z' axes and by rotationof the plate around the z'-axis through an angle in the range -20°through -10° or +10° through +20°, the plate having a vibrationalportion having a tuning fork shape and being vibratable in a torsionalmode of vibration, a supporting portion for supporting the resonator,and a bridge portion interconnecting the vibrational and supportingportions such that the vibrational portion can undergo torsional modevibration relative to the supporting portion during use of theresonator, the resonator having a thickness-to-width ratio R_(zx) =z₀/x₀ within the range of 0.6 through 1.1, and the resonator having afirst order temperature coefficient α of approximately zero around roomtemperature.
 8. A torsional quartz crytal tuning fork resonatoraccording to claim 7; including electrodes on the vibrational,supporting and bridge portions for exciting the vibrational portion intotorsional mode vibration.
 9. A torsional quartz crystal tuning forkresonator according to claim 7; wherein the bridge portion is connectedto the vibrational portion at an intermediate position therealong.
 10. Atorsional quartz crystal tuning fork resonator according to claim 7;wherein the vibrational, supporting and bridge portions comprisechemically etched portions of the Z-cut plate.
 11. A torsional quartzcrystal tuning fork resonator according to claim 1; wherein theresonator has a second order temperature coefficient β in the range of-2.6 through -1.2×10⁻⁸ /°C.².
 12. A torsional quartz crystal tuning forkresonator according to claim 3; wherein the resonator has a second ordertemperature coefficient β in the range of -2.6 through -1.2×10⁻⁸ /°C.².13. A torsional quartz crystal tuning fork resonator according to claim6; wherein the resonator has a second order temperature coefficient β inthe range of -2.6 through -1.2×10⁻⁸ /C.².
 14. A torsional quartz crystaltuning fork resonator according to claim 7; wherein the resonator has asecond order temperature coefficient β in the range of -2.6 through-1.2×10⁻⁸ /°C.².